* Q.>if x= 2/3 and x= -3 are the roots of the equation ax^{2 }+7x+b=0, find the value of a and b. *

Given, and *x* = – 3 are the roots of the quadratic equation .

...(1)

Putting in equation (1), we get

Putting *x* = – 3 in equation (1), we get

⇒ 9*a* – 21 + *b* = 0

⇒ 9*a* + *b* = 21

⇒ *b* = 21 – 9*a *...(3)

Solving (2) and (3), we get

4*a* + 9 ( 21 – 9*a*) = – 42

⇒ 4*a* + 189 – 81*a* = – 42

⇒ –77*a =* – 42 – 189 = – 231

⇒ *a* = 3

Putting the value of *a* in (3), we get

*b* = 21 – 9 × 3 = 21 – 27 = – 6

Thus, the value of *a* and *b* is 3 and – 6 respectively.

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